External Pressure on half of a PV 1

[qwicker]

Hello,

For those who read my last thread, I have completely solved it. Thanks to those who helped.

My new quesion is merely conceptual. I have a pressure vessel with an internal pressure that will have only HALF of its external shell subjected to a very high external pressure. I am not sure how to account for the fact that only half of the shell sees this pressure. Can I just plug the external pressure into the Stress equations for a pressure vessel or do I have to half it or double it etc. Any help/ideas are appreciated.

 

[BusaJames]

Well if you want purely stress, you'd leave it. Stress is pressure per unit area, right? So you're only seeing half the pressure because only half is exposed, but you only have half the area as well. So the stress on the exposed side is the same whether or not the opposite side is exposed. This all sounds good in my head at least

 

[JStephen]

The ASME equations are set up to consider buckling in a shell and/or stiffeners, assuming the pressure acts all around. If the pressure is applied over only part of the circumference, you'd still have the possibility of buckling, but you also introduce some large bending loads somewhere (exact nature would depend on the geometry of the vessel and loading).

 

[mtnengr]

Qwicker:

You need to be a little more precise on the problem. If the external pressure is an axisymmetric pressure along half the length of the cylinder, a discontinuity stress from bending will be present. If the external pressure is distributed over half of the circumfence, non-axisymmetric surface pressures can be determined. The distibution would be based upon the manner of the applied pressure and over what portion of the cylinder. The surface pressures could be constant over the cylinder from -90 degrees to +90 degrees or could have a cosine distribution.

The boundary conditions at the end of the cylinder are also very important. If the ends are capped, discontinuity stresses at the juncture point can result in very high bending stresses in the region.

These problems, especially buckling problems, need to be solved using specific computer codes designed for this class of problem. There are a number of shell codes that have been described in the past. You can use the FEM for this purpose. There are a few commercial codes available. However, some expreience is required to understand the results.

The final question remains as to the state of stress just prior to buckling. You may have to consider either geometric or matrerial nonlinearity.

 

[qwicker]

Thanks everyone for helping.
Mtnengr: The load is distributed on half of the length, meaning it is applied on half of the outter surface area. The PV is also open ended.

What I have done though is just assumed that the pressure acts on the entire outside and just ran calculations like that. It is only for a rough estimation. I dont want to btoehr with extensiv coding or analysis in order to figure it out. I do have Ansys, so maybe I will try that. Thank you

 

[mtnengr]

Quicker:

If the shell has a length greater than beta (L) > 6, the buckling load should correspond to n=2 as the minimum load.
Beta = 1.28/(Rt)**1/2.

You should use the length of the applied load.

 

[MintJulep]

I'm having trouble envisioning how this would be physically possible.

 

[qwicker]

Hmm I wish I could upload pictures here because I created a great little illustration at work to help explain the problem to others. More detail: I have a "pin" that is inside a bore hole. The bore is larger than the pin. The pin will be pulled in tension perpendicular to the direction that it is inserted into the bore. Thus, only half of the pin's outer surface will be in conctact with the inner surface of the bore. Think of 2 circles, 1 inside the other. The inside circle is slightly smaller and is touching the inside surface.

 

[MintJulep]

Ok. Nice mental picture.

Now I'm having trouble seeing how a pressure vessel analysis technique could possibly be appropriate to that.

 

[qwicker]

Ok well the "pin" is actually a press fitted pin inside a sleeve. This there is internal contact pressure in teh sleeve. I am modeling the contact force between the outside of the sleeve and the inside of the bore. Its like a pin inside a sleeve inside a bore which is slightly larger than the sleeve. I am modeling the bore/sleeve pressure as an external pressure on the pin/sleeve "pressure vessel"

 

[mtnengr]

MintJulep: To gain an understanding of the bifurcation process for cylindrical shells of revolution subjected an external pressure into another state, may I suggest that you examine: Paragraph 83, Timoshenko, Theory of Elastic Stability, Eng. Soc Monographs.

Quicker: I do not think that your model of an interference problem of a pin in a sleeve can be addressed as a cylinder subjected to an external pressure. You need to model both external and internal components. Their compliances will dictate the state of stress and their response. The external restraint of the outer diameter will be defined as a contact problem. This now becomes a geometric nonlinear contact problem, not a buckling of a shell. If the interference is large enough, plastic flow may be possible.

 

[JStephen]

Unless your pin is very very thin-walled, I doubt you're likely to get into the kind of situation anticipated in pressure vessel work.